It's really not necessary to use Simpson's Rule. Find an volume by cross-section. In order to do that, you need to develop an equation for the area, in this case a square. By the equations you gave, the length of one side of the square would be [tex]4-[(x^2)-2][/tex]. Since the cross-sections are perpendicular to the x axis. You can leave the function as is since it is already in terms of x. So the formula for volume by cross-sections is

[tex]\int^a_b A(x)\delta x[/tex]

so after finding your a and b, (set the equations equal to each other)